English

Relationships Between the Bergman Kernels of Hartogs Domains and Their Base

Complex Variables 2024-06-25 v2

Abstract

We explore the relationship between the Bergman kernel of a Hartogs domain and weighted Bergman kernels over its base domain. In particular we develop a representation of the Bergman kernel of a Hartogs domain as a series involving weighted Bergman kernels over its base, as well as a "transformation" formula for some weighted Bergman kernels. Other relationships of this type are presented.

Keywords

Cite

@article{arxiv.2208.14291,
  title  = {Relationships Between the Bergman Kernels of Hartogs Domains and Their Base},
  author = {Blake J. Boudreaux},
  journal= {arXiv preprint arXiv:2208.14291},
  year   = {2024}
}